The Church of England plans to encourage its schools to offer more places to non-Christians. The Rt Rev John Pritchard, who is chair of the CoE's board of education and the bishop of Oxford, said he was urging headteachers to allocate no more than 10% of places to practising Anglicans.

At the moment, if a state-funded church school is oversubscribed, it can select pupils based on their and their parents' religious observance. If it is not oversubscribed, it must take those pupils who apply. The change could end the practice of parents attending services purely to secure their child a place at a popular CoE school.

Pritchard told the Times Educational Supplement that he wanted CoE schools to be "as open as they can be".

"Every school will have a policy that has a proportion of places for church youngsters … What I am saying is that the number ought to be minimised because our primary function and our privilege is to serve the wider community. Ultimately, I hope we can get the number of reserved places right down to 10%. It goes back to what we see the mission of the church as being. I don't think the mission generally is about collecting nice Christians into safe places."

About half of the 4,800 CoE schools set their own admissions criteria. The CoE cannot force its schools to change their admissions practices but it will issue guidance this summer designed to encourage them to do so.

Professor Anne West, an education expert at the LSE, said the change could have "the biggest impact on admissions to CoE schools in a generation".

Pritchard said offering a greater proportion of places to pupils whose families do not attend church might lead to a drop in CoE schools' exam results.

"We may not get the startling results that some church schools do because we get some very able children, but we will make a difference to people's lives," he said.

Terry Sanderson, president of the National Secular Society, said Pritchard had become the first high-profile Anglican to admit that church schools achieved "league-topping results by using privileged admissions criteria to select the best pupils".

Rabbi Dr Jonathan Romain, chair of Accord, which campaigns to end religious discrimination in school admissions, said current practices had meant that religion and discrimination in schools had "become almost synonymous".

"Schools should be inclusive and tolerant and no state-funded school should be allowed to discriminate on the grounds of religion for any of their teacher posts or any pupil places," he said.

The previous government tried to ensure that a quarter of all places at new faith schools were for pupils of other faiths or no faith, but lobbying from the Catholic church forced ministers to drop the plans.